CCP4 wiki - User contributions [en]

Template:Cite book

2008-02-18T15:31:15Z

Ralf: New page: {{cite book | last = | first = | authorlink = | coauthors = | title = | publisher = | date = | location = | pages = | url = | doi = | id = | isbn = }}

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R-factors

2008-02-18T15:09:05Z

Ralf:

Historically, R-factors were introduced by ... ???

== Definitions ==
=== Data quality indicators ===
In the following, all sums over hkl extend only over unique reflections with more than one observation!
* Rsym and Rmerge - the formula for both is:
<math>
R = \frac{\sum_{hkl} \sum_{j} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}
</math>
where <math>\langle I_{hkl}\rangle</math> is the average of symmetry- (or Friedel-) related observations of a unique reflection.

It can be shown that this formula results in higher R-factors when the redundancy is higher <ref name="DiKa97">K. Diederichs and P.A. Karplus (1997). Improved R-factors for diffraction data analysis in macromolecular crystallography. Nature Struct. Biol. 4, 269-275 [http://strucbio.biologie.uni-konstanz.de/strucbio/files/nsb-1997.pdf]</ref>. In other words, low-redundancy datasets appear better than high-redundancy ones, which obviously violates the intention of having an indicator of data quality!
* Redundancy-independant version of the above:
<math>
R_{meas} = \frac{\sum_{hkl} \sqrt \frac{n}{n-1} \sum_{j=1}^{n} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}
</math>
which unfortunately results in higher (but more realistic) numerical values than Rsym / Rmerge <ref name="DiKa97"/> (M.S. Weiss and R. Hilgenfeld (1997) On the use of the merging R-factor as a quality indicator for X-ray data. J. Appl. Crystallogr. 30, 203-205[http://dx.doi.org/10.1107/S0021889897003907]).

* measuring quality of averaged intensities/amplitudes:

for intensities use (M.S. Weiss. Global indicators of X-ray data quality. J. Appl. Cryst. (2001). 34, 130-135 [http://dx.doi.org/10.1107/S0021889800018227])
<math>
R_{p.i.m.} = \frac{\sum_{hkl} \sqrt \frac{1}{n} \sum_{j=1}^{n} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}
</math>

<math>R_{mrgd-I}</math> is similarly defined in Diederichs and Karplus <ref name="DiKa97"/>.

Similarly, one should use Rmrgd-F as a quality indicator for amplitudes <ref name="DiKa97"/>, which may be calculated as:
<math>
R_{mrgd-F} = \frac{\sum_{hkl} \sqrt \frac{1}{n} \sum_{j=1}^{n} \vert F_{hkl,j}-\langle F_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}F_{hkl,j}}
</math>
with <math>\langle F_{hkl}\rangle</math> defined analogously as <math>\langle I_{hkl}\rangle</math>.

=== Model quality indicators ===
* R and Rfree : the formula for both is
<math>
R=\frac{\sum_{hkl}\vert F_{hkl}^{obs}-F_{hkl}^{calc}\vert}{\sum_{hkl} F_{hkl}^{obs}}
</math>
 
 
where <math>F_{hkl}^{obs}</math> and <math>F_{hkl}^{calc}</math> have to be scaled w.r.t. each other. R and Rfree differ in the set of reflections they are calculated from: R is calculated for the [[working set]], whereas Rfree is calculated for the [[test set]].
== what do R-factors try to measure, and how to interpret their values? ==
* relative deviation of
=== Data quality ===
* typical values: ...
=== Model quality ===

==== Relation between R and Rfree as a function of resolution ====

References:
* Tickle IJ, Laskowski RA and Moss DS. Rfree and the Rfree Ratio. I. Derivation of Expected Values of Cross-Validation Residuals Used in Macromolecular Least-Squares Refinement. Acta Cryst. (1998). D54, 547-557 [http://dx.doi.org/10.1107/S0907444997013875]

* Tickle IJ, Laskowski RA and Moss DS. Rfree and the Rfree ratio. II. Calculation of the expected values and variances of cross-validation statistics in macromolecular least-squares refinement. Acta Cryst. (2000). D56, 442-450 [http://dx.doi.org/10.1107/S0907444999016868]

* GJ Kleywegt and TA Jones (2002). Homo Crystallographicus - Quo vadis? Structure 10, 465-472. (reprint from http://xray.bmc.uu.se/cgi-bin/gerard/reprint_mailer.pl?pref=65)
- formula from that paper: Rfree = 1.065*R + 0.036

- plot with empirical data: http://xray.bmc.uu.se/gerard/supmat/rfree2000/rfminusr_vs_resolution.gif

- many more plots: http://xray.bmc.uu.se/gerard/supmat/rfree2000

- harry plotter (java): http://xray.bmc.uu.se/gerard/supmat/rfree2000/plotter.html

== what kinds of problems exist with these indicators? ==
- (Rsym / Rmerge ) should not be used, Rmeas should be used instead (explain why ?)

- R/Rfree and NCS: reflections in work and test set are not independant

==Notes==
<references/>

R-factors

2008-02-14T13:51:47Z

Ralf: /* Data quality indicators */

Historically, R-factors were introduced by ...

== Definitions ==
=== Data quality indicators ===
* Rsym and Rmerge : the formula is
<math>
R_{merge} = \frac{\sum_{hkl}\vert I_{hkl}-\langle I_{hkl}\rangle\vert}{\sum_{hkl}I_{hkl}}
</math>
 
 
<math>
R=\frac{\sum_{hkl_{unique}}\vert F_{hkl}^{(obs)}-F_{hkl}^{(calc)}\vert}{\sum_{hkl_{unique}} F_{hkl}^{(obs)}}
</math>
* Redundancy-independant version of the above: Rmeas
* measuring quality of averaged intensities/amplitudes: Rp.i.m. and Rmrgd-F

=== Model quality indicators ===
* R and Rfree : the formula is (LaTex please )

== what do R-factors try to measure, and how to interpret their values? ==
* relative deviation of
=== Data quality ===
* typical values: ...
=== Model quality ===

== what kind of problems exist with these indicators? ==
- (Rsym / Rmerge ) should not be used, Rmeas should be used instead (explain why ?)

- R/Rfree and NCS: reflections in work and test set are not independant

R-factors

2008-02-14T13:47:53Z

Ralf: /* Data quality indicators */

Historically, R-factors were introduced by ...

== Definitions ==
=== Data quality indicators ===
* Rsym and Rmerge : the formula is (someone with LaTex knowledge please don't hesitate to fill in the formula!)
<math>
R_{merge} = \frac{\sum_{hkl}\vert I_{hkl}-\langle I_{hkl}\rangle\vert}{\sum_{hkl}I_{hkl}}
</math>
* Redundancy-independant version of the above: Rmeas
* measuring quality of averaged intensities/amplitudes: Rp.i.m. and Rmrgd-F

=== Model quality indicators ===
* R and Rfree : the formula is (LaTex please )

== what do R-factors try to measure, and how to interpret their values? ==
* relative deviation of
=== Data quality ===
* typical values: ...
=== Model quality ===

== what kind of problems exist with these indicators? ==
- (Rsym / Rmerge ) should not be used, Rmeas should be used instead (explain why ?)

- R/Rfree and NCS: reflections in work and test set are not independant

Test

2008-02-05T09:21:41Z

Ralf:

We test tex:

<math>
F_{hkl} = \sum_{i=1}^{N} e^{-2\pi\imath\left( h\frac{x}{a}+k\frac{y}{b}+l\frac{z}{c}\right)}
</math>

[[Image:Acrb.jpg|thumb|test]]

All crystals should look like this (or better)
[[Image:xtals.jpg||pretty xtals]]

Problem? - I tried uploading xtals.png but Wiki does not let me upload, quoting that 'wrong file type or extension' - yet it allowed me to load up the same image in jpg format. Png is a nice (some would even say the best) format so it'd be good to be able to use it! -AGE
This is fixed now. --[[User:Kay|Kay]] 10:12, 5 February 2008 (CET)
 
Remark:
MIME type of PNG files was not correctly identified. To fix this, we added the lines
# PNG
1 string PNG image/png
to the file /etc/httpd/conf/magic

Main Page

2008-02-01T11:06:20Z

Ralf:

== Getting started ==

Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.
* [[Special:Allpages|All pages]] - list of all pages of this wiki

Test

2008-02-01T11:03:12Z

Ralf:

We test tex:

<math>
F_{hkl} = \sum_{i=1}^{N} e^{-2\pi\imath\left( h\frac{x}{a}+k\frac{y}{b}+l\frac{z}{c}\right)}
</math>

[[Image:Acrb.jpg|thumb|test]]

File:Acrb.jpg

2008-02-01T11:00:27Z

Ralf:

Test

2008-02-01T11:00:15Z

Ralf: New page: We test tex: <math> F_{hkl} = \sum_{i=1}^{N} e^{-2\pi\imath\left( h\frac{x}{a}+k\frac{y}{b}+l\frac{z}{c}\right)} </math>

We test tex:

<math>
F_{hkl} = \sum_{i=1}^{N} e^{-2\pi\imath\left( h\frac{x}{a}+k\frac{y}{b}+l\frac{z}{c}\right)}
</math>